Commutators of multilinear Calderon-Zygmund operators with kernels of Dini's type on generalized weighted Morrey spaces and applications

Let T be a multilinear Calderon-Zygmund operator of type omega with omega being nondecreasing and satisfying a kind of Dini's type condition and T-Pi(b)over right arrow be the iterated commutators of the operator T with BMOm functions. The generalized weighted Morrey strong and weak L(log L)-type endpoint estimates for T and T-Pi(b)over right arrow with multiple weights are established. As applications multiple weighted Morrey estimates for iterated commutators of bilinear pseudo-differential operators and paraproducts with mild regularity are given.